The Lindelöf number of functional spaces on monolithic compacta
type: Item
instance of: scholarly article
title: The Lindelöf number of functional spaces on monolithic compacta
zbMATH Open document ID: 1404.54015
DOI: 10.3103/S0027132218030063
author: D. P. Baturov
author: Evgenii Reznichenko
published in: Moscow University Mathematics Bulletin
publication date: 2018-10-10T00:00:00Z
review text: Let \(X\) be a Hausdorff compact space and \(\tau\) an infinite cardinal. Denote by \(C_{c(\tau)}(X)\) the space of continuous real-valued functions on \(X\) with the topology of uniform convergence on compacta of weight \(\leq \tau\). The authors investigate the Lindelöf number \(\ell (C_{c(\tau)}(X))\) of this space. It is proved: (1) If \(X\) is \(\tau\)-monolithic and its tightness is \(\leq \tau\), then \(\ell(C_{c(\tau^+)}(X)) \leq \tau^+\); in particular, if the tightness of \(X\) is \(\leq \tau\), then \(\ell(C_{c(2^{\tau})}(X)) \leq 2^{\tau}\). (Recall that a space \(X\) is \(\tau\)-monolithic if for every \(A \subset X\) of cardinality \(\leq \tau\), the network weight of \(\overline{A}\) does not exceed \(\tau\)); (2) Under the assumption that no Aronszajn \(\tau^+\)-tree exists, \(\ell(C_{c(\tau)}(X)) \leq \tau\) whenever \(X\) is zero-dimensional, \(\tau\)-monolithic and its tightness is \(\leq \tau\).
Mathematics Subject Classification ID: 54C35
Mathematics Subject Classification ID: 54A25
Mathematics Subject Classification ID: 54D20
zbMATH DE Number: 6951205
zbMATH Keywords: Lindelöf number
zbMATH Keywords: \(\tau\)-monolithic
zbMATH Keywords: tightness
zbMATH Keywords: Aronszajn tree
reviewed by: Ljubiša D. R. Kočinac
MaRDI profile type: Publication
cites work: Q4150804
cites work: Q2957940
full work available at URL: s0027132218030063
OpenAlex ID: W2831540304
description: scientific article; zbMATH DE number 6951205